anb2016 Posted March 23, 2015 Report Share Posted March 23, 2015 Ok so I was thinking about radians and then I thought why is radians in terms of a radius?. Why not use the diameter to derive an angle measurement? I'll call it diametrans for now. so since one full turn is equal to 2pi radians, it would be Pi "diametrans" and half a turn would be π/2 diametrans and so on. I guess its not groundbreaking or anything but did I think of a viable new angle unit or has it already been made but I don't know of it? Or does it not make sense? 1 Reply Link to post Share on other sites More sharing options...
anb2016 Posted March 23, 2015 Author Report Share Posted March 23, 2015 Its basically the same as radians except times two. I just wonder why the person who created radians used radius rather than diameter. Reply Link to post Share on other sites More sharing options...
IbTrojan Posted March 23, 2015 Report Share Posted March 23, 2015 It makes sense but I think maybe because dividing each value by two would create more fractions making calculations more complicated than they already are. Like, having 180 degrees as pi is a lot easier than having it as pi/2 because then when we get to the acute angles, the values get ridiculous, I doubt it hasn't been discovered before but again, an interesting point to discuss 1 Reply Link to post Share on other sites More sharing options...
anb2016 Posted March 23, 2015 Author Report Share Posted March 23, 2015 Yeah I didn't think about that. But would it really make it harder to work with though? for example 30 degrees would just be π/24 diametrans. Not better or worse just different. I guess trigonometric functions would be weirder too cause cos(0 would be 1/2 diametrans. And the amplitude of sin and cos graphs would be 1/2 Reply Link to post Share on other sites More sharing options...
IbTrojan Posted March 23, 2015 Report Share Posted March 23, 2015 Also, they'd have to make a new function in calculators for "diametrans" as well and if they and radians serve the same purpose, might as well stick with the simpler of the two, you know?I'm not trying to knock you down, just throwing out my thoughts. 1 Reply Link to post Share on other sites More sharing options...
anb2016 Posted March 23, 2015 Author Report Share Posted March 23, 2015 Yeah you're completely right! I know it would be useless to actually use. I was just wondering if it would work and why the creator of radians used radius instead of diameter to measure angles 1 Reply Link to post Share on other sites More sharing options...
IbTrojan Posted March 23, 2015 Report Share Posted March 23, 2015 Hmm, those are good questions to ask. Maybe because the radius is used more than the diameter? It should work for sure though...but you'd have to see the mathematics behind radians to see if the same process could be used for this new measurement. 1 Reply Link to post Share on other sites More sharing options...
Vioh Posted March 23, 2015 Report Share Posted March 23, 2015 Very interesting question. One answer that I can think of is because the radius is the property of a circle that will never disappear if you divide the circle into many sections (using the normal way of dividing of course). Let's say that you divide the circle into 4 equal sections, then the diameter would disappear, but you can still see the radius.This doesn't make too much difference. But if you have one forth of a pie, would you rather measure the radius and then times it by two to get the diameter, before you can do any computations with it? or would you rather measure the radius and then do calculations with it directly? By the way, there is also another debate that is similar to this. But instead of radius vs. diameter, it is pi vs. tau. Here's the video. Check it out!https://www.youtube.com/watch?v=83ofi_L6eAo 1 Reply Link to post Share on other sites More sharing options...
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